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Putnam
1941 Putnam
A1
Putnam 1941 A1
Putnam 1941 A1
Source: Putnam 1941
February 23, 2022
Putnam
algebra
polynomial
Problem Statement
Prove that the polynomial
(
a
−
x
)
6
−
3
a
(
a
−
x
)
5
+
5
2
a
2
(
a
−
x
)
4
−
1
2
a
4
(
a
−
x
)
2
(a-x)^6 -3a(a-x)^5 +\frac{5}{2} a^2 (a-x)^4 -\frac{1}{2} a^4 (a-x)^2
(
a
−
x
)
6
−
3
a
(
a
−
x
)
5
+
2
5
a
2
(
a
−
x
)
4
−
2
1
a
4
(
a
−
x
)
2
takes only negative values for
0
<
x
<
a
0<x<a
0
<
x
<
a
.
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